The general aim of our research is to discover the principles that determine i) the three-dimensional structure of proteins, and ii) how proteins evolve. Nearly all proteins are close packed assemblies of Alpha-helices and Beta-pleated sheets. Therefore their three-dimensional structure is determined by the shape of the surfaces of the component secondary structures. We have shown how simple models can be used to explain the manner in which Alpha-helices are observed to pack on other Alpha-helices and Beta-pleated sheets. The models were developed by a detailed analysis of the residue to residue contacts and conformations that occur in known protein structures, using interactive computer graphics and numerical calculations. We now wish to similarly determine the principles that govern the packing and assembly of Beta-pleated sheets in proteins. An understanding of the principles that determine the structure of proteins will lead to a better appreciation of how proteins evolve. We have shown that during the evolution of the globins, mutations in their interior have changed the relative positions to homologous pairs of Alpha-helices by rigid body shifts up to 7angstroms and 30degrees. The activity of the molecule is retained by coupling these changes so the geometry of the haem pocket is almost constant. We now wish to extend this work. First, we will determine the exact structural changes that have occurred during the evolution of proteins formed from Beta-sheets (serine proteases, immunoglobin domains, etc.) and from Alpha-helices and Beta-sheets (NAD coenzyme binding domains, etc.), and relate these changes to the difference in the sequences. Second, we will use these results and those of other workers to derive general principles for the evolution of protein structures.